SOLUTION: how long will it take $500 to double it it is invested at 12% compounded quarterly?

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Question 372469: how long will it take $500 to double it it is invested at 12% compounded quarterly?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


1000=500%281%2B0.12%2F4%29%5E%284%2At%29 Plug in A=1000 (double the initial investment of $500), P=500, r=0.12 (the decimal equivalent of 12%), and n=4.


1000=500%281%2B0.03%29%5E%284%2At%29 Evaluate 0.12%2F4 to get 0.03


1000=500%281.03%29%5E%284%2At%29 Add 1 to 0.03 to get 1.03


1000%2F500=%281.03%29%5E%284%2At%29 Divide both sides by 500.


2=%281.03%29%5E%284%2At%29 Evaluate 1000%2F500 to get 2.


ln%282%29=ln%28%281.03%29%5E%284%2At%29%29 Take the natural log of both sides.


ln%282%29=4%2At%2Aln%281.03%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


ln%282%29%2Fln%281.03%29=4%2At Divide both sides by ln%281.03%29.


0.693147180559945%2Fln%281.03%29=4%2At Evaluate the natural log of 2 to get 0.693147180559945.


0.693147180559945%2F0.0295588022415444=4%2At Evaluate the natural log of 1.03 to get 0.0295588022415444.


23.4497722504377=4%2At Divide.


23.4497722504377%2F4=t Divide both sides by 4 to isolate "t".


5.86244306260943=t Divide.


t=5.86244306260943 Rearrange the equation.


t=6 Round to the nearest whole number (ie to the nearest whole year).


So it will take about 6 years for the investment to double.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim